Facebook CEO Mark Zuckerberg would have earned a slightly improved grade this year for his leadership of the social media company, Yale School of Management Senior Associate Dean Jeffrey Sonnenfeld says.

''He would be getting a very generous B-minus," Sonnenfeld said. "I graded him higher than I did this time last year because he has done very well. Zuckerberg has done really well in getting out from under the hood, being more public."

Sonnenfeld had previously given Mark Zuckerberg a C-minus.

On CNBC's "Fast Money," Sonnenfeld said that Zuckerberg had earned extra credit for hiring Sheryl Sandberg as chief operating officer, as well as for his philanthropy.

Facebook's business performance, too, was more positive.

"The mobile ad revenue - which was zero this time last year, then we saw it hit 11 percent, then 26 percent it hit last quarter and now up to 30 percent - is fantastic," Sonnenfeld said. "They doubled the share of mobile minutes, and that's great."

But, challenges remain.

Sonnenfeld said that legal issues with the Securities and Exchange Commission were hanging over the company's outlook.

"They still have some major challenges to take on and trying to use the incredible user database that they have. They've still not tapped into that," he added. "Their search engine promise has been much-touted in what they can do with semantic search, but we haven't seen it yet."

Sonnenfeld also said that it was possible to continue to run a successful social media company without a soaring stock price, citing Cisco CEO John Chambers and his leadership at "a very solid company" with a share price trading at one-quarter of its March 2000 high near $80.

"We have to move away from the yardsticks that were wrong," he said. "So, I think we have to separate the performance of Zuckerberg and Sheryl Sandberg and the leadership and this company from that overinflated stock price. It's a different issue."

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